Theorems · Definition · combinatorics
Quiver.Hom.toPath
{V : Type u_1} → [inst : Quiver V] → {a b : V} → (a ⟶ b) → Quiver.Path a bAn arrow viewed as a path of length one.
- Defined in
- Mathlib.Combinatorics.Quiver.Path
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Quiverstatement and proof · cited by 405
- Quiver.Pathstatement · cited by 166
Cited by52
Results whose statement or proof uses this declaration.
- CategoryTheory.Paths.ofproof · cited by 20
- CategoryTheory.Cat.FreeRefl.homMkproof · cited by 13
- CategoryTheory.Paths.ext_functorstatement and proof · cited by 6
- CategoryTheory.composePath_toPathstatement · cited by 5
- Quiver.FreeGroupoid.lift_uniqueproof · cited by 3
- Quiver.Path.eq_toPath_comp_of_length_eq_succstatement and proof · cited by 2
- CategoryTheory.Localization.Construction.morphismProperty_eq_topproof · cited by 2
- Quiver.Path.reverse_compproof · cited by 2
- CategoryTheory.Paths.liftNatIsostatement and proof · cited by 2
- CategoryTheory.toQuotientPathsproof · cited by 2
- CategoryTheory.MorphismProperty.toPath_mem_pathsstatement · cited by 1
- Quiver.Path.exists_notMem_mem_hom_path_path_of_notMem_memstatement and proof · cited by 1